Finance/Accounting Math: If a product margin percentage is 60%. How much is the product margin % after a -10% discount? I would like to know the formula to calculate margin percentage after a discount. I can figure this out in excel manually but would be great to know the formula to figure it out quickly as a back-of-the-envelope calculation? Just to clarify that the question is about the margin %, not the markup % Margin % = 1 - (Cost per unit/Selling Price) Mark up % = (Selling price/Cost per unit) - 1

First of all we have $1-\frac{c}s=0.6=m^{bd}\Rightarrow \frac{c}s=0.4 \qquad (*)$

After a 10% discount the equation is $100-\frac{c}{0.9s}\cdot 100=m^{ad}$

$m^{bd}$ is the margin before discount in percentage

$m^{ad}$ is the margin after discount in percentage

Then $\frac1{0.9}=\frac{10}9$.

$\frac99-\frac{10}{9}\frac{c}s=x$

Inserting the value of $\frac{c}s$ from $(*)$

$m^{ad}=\frac99-\frac{10}{9}\cdot \frac4{10}=\frac59\approx 0.56$

Therefore the formula is $$\boxed{m^{ad}=100\left(1-\frac{100}{100-d}\cdot \left(1-{\frac{m^{bd}}{100}} \right)\right)}$$

$d:$= discount in percentage